Worksheet: Heat Engines

In this worksheet, we will practice comparing the work done by heat engines with different reservoir temperatures ratios and calculating their efficiencies.

Q1:

What is the efficiency of a heat engine that has constant reservoir temperatures of and ? Answer to three significant figures.

Q2:

The graph shows the relationship between the loss of the internal energy of the high-temperature reservoir of a heat engine and the gain in internal energy of the heat engineβs low-temperature reservoir for different values of , the ratio of the temperatures of the reservoirs. Which is the greatest temperature ratio?

• A
• B
• C

Q3:

A heat engine is represented in the diagram, showing the quantities associated with its operation. Which of the following formulas most correctly represents the relationship between , , and ?

• A
• B
• C
• D
• E

Q4:

The reservoirs of a heat engine consist of equal masses of water. The reservoirs exchange energy while being maintained at constant temperatures. The changes with time of the internal energies of the reservoirs and the work done by the heat engine are shown in the diagrams. The purple line shows the high-temperature reservoir, the blue line shows the low-temperature reservoir, and the red line shows the work output. Which diagram correctly shows the energy changes over time?

• A
• B
• C
• D

Q5:

What is the efficiency of a heat engine that supplies 400 J of useful work when its high temperature reservoir heats its low temperature by 1,000 J?

Q6:

The graph shows the relationship between the loss of internal energy of the high temperature reservoir of a heat engine and , the work done by the heat engine, depending on the value of , the ratio of the temperatures of the reservoirs. Which is the greatest temperature ratio?

• AI
• BII
• CIII

Q7:

The reservoirs of a heat engine consist of equal masses of water. The reservoirs heat each other and reach an equilibrium temperature. The changes of the internal energies of the reservoirs and of the work done by the heat engine with time are shown in the diagrams. The purple line shows the high-temperature reservoir, the blue line shows the low-temperature reservoir, and the red line shows the work output. Which diagram correctly shows the energy changes over time?

• A
• B
• C
• D

Q8:

The diagram shows a Carnot cycle for a gas, consisting of four changes. Two of the changes are an adiabatic expansion and an adiabatic compression. The other two changes are an isothermal expansion and an isothermal compression, occurring at different temperatures

.

During which change of the gas is the gas heated?

• AChange IV
• BChange II
• CChange III
• DChange I

During which change of the gas is the gas cooled?

• AChange IV
• BChange I
• CChange II
• DChange III

During which change of the gas is work done by the gas?

• AChange IV
• BChange II
• CChange III
• DChange I

During which change of the gas is work done on the gas?

• AChange III
• BChange II
• CChange I
• DChange IV

Which change of the gas begins with the gas at the highest temperature involved in the cycle?

• AChange III
• BChange IV
• CChange II
• DChange I

Is the net work done by the gas during the cycle less than, equal to, or greater than the net heating of the gas?

• AThe net work done is equal to the net heating.
• BThe net work done is greater than the net heating.
• CThe net work done is less than the net heating.